On Colorful Bin Packing Games

We consider colorful bin packing games in which selfish players control a set of items which are to be packed into a minimum number of unit capacity bins. Each item has one of $m\geq 2$ colors and cannot be packed next to an item of the same color. All bins have the same unitary cost which is shared among the items it contains, so that players are interested in selecting a bin of minimum shared cost. We adopt two standard cost sharing functions: the egalitarian cost function which equally shares the cost of a bin among the items it contains, and the proportional cost function which shares the cost of a bin among the items it contains proportionally to their sizes. Although, under both cost functions, colorful bin packing games do not converge in general to a (pure) Nash equilibrium, we show that Nash equilibria are guaranteed to exist and we design an algorithm for computing a Nash equilibrium whose running time is polynomial under the egalitarian cost function and pseudo-polynomial for a constant number of colors under the proportional one. We also provide a complete characterization of the efficiency of Nash equilibria under both cost functions for general games, by showing that the prices of anarchy and stability are unbounded when $m\geq 3$ while they are equal to 3 for black and white games, where $m=2$. We finally focus on games with uniform sizes (i.e., all items have the same size) for which the two cost functions coincide. We show again a tight characterization of the efficiency of Nash equilibria and design an algorithm which returns Nash equilibria with best achievable performance

On the use of bianisotropic huygens' metasurfaces to build leaky-wave antennas

The Electromagnetics AcademyHuygens' metasurfaces are considered a powerful tool to achieve anomalous electromagnetic field transformations. They consist of an artifcial surface built of pairs of collocated electric and magetic dipoles that force the boundary conditions for the desired transformation to be ful lled [1]. Despite their possibilities, the achievable transformations must ful l some conditions. In [2] it was shown that Huygens' metasurfaces with passive and lossless particles can achieve an arbitrary field transformation provided that the power is conserved at each point of the metasurface and there is wave impedance matching. However, it was shown in [3], that by introducing bianisotropy of the omega-type, the matching condition can be suppressed, which allows the control of both the transmission and rejection coe cients on the metasurface.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Causal perturbation theory in terms of retarded products, and a proof of the Action Ward Identity

In the framework of perturbative algebraic quantum field theory a local construction of interacting fields in terms of retarded products is performed, based on earlier work of Steinmann. In our formalism the entries of the retarded products are local functionals of the off shell classical fields, and we prove that the interacting fields depend only on the action and not on terms in the Lagrangian which are total derivatives, thus providing a proof of Stora's 'Action Ward Identity'. The theory depends on free parameters which flow under the renormalization group. This flow can be derived in our local framework independently of the infrared behavior, as was first established by Hollands and Wald. We explicitly compute non-trivial examples for the renormalization of the interaction and the field.Comment: 76 pages, to appear in Rev. Math. Phy

Abstract Tensor Systems as Monoidal Categories

The primary contribution of this paper is to give a formal, categorical treatment to Penrose's abstract tensor notation, in the context of traced symmetric monoidal categories. To do so, we introduce a typed, sum-free version of an abstract tensor system and demonstrate the construction of its associated category. We then show that the associated category of the free abstract tensor system is in fact the free traced symmetric monoidal category on a monoidal signature. A notable consequence of this result is a simple proof for the soundness and completeness of the diagrammatic language for traced symmetric monoidal categories.Comment: Dedicated to Joachim Lambek on the occasion of his 90th birthda

Gauge invariance of massless QED

A simple general proof of gauge invariance in QED is given in the framework of causal perturbation theory. It illustrates a method which can also be used in non-abelian gauge theories.Comment: 7 pages, TEX-file, Zuerich University Preprint ZU-TH-33/199

Factors Affecting the Corporate Decision-Making Process of Air Transport Manufacturers

Fuel economy is a pivotal question influencing the future sale and utilization of commercial aircraft. The NASA Aircraft Energy Efficiency (ACEE) Program Office has a program intended to accelerate the readiness of advanced technologies for energy efficient aircraft. Because the decision to develop a new airframe or engine is a major financial hazard for manufacturers, it is important to know what factors influence the decision making process. A method is described for identifying and ranking individuals and organizations involved at each stage of commercial air transport development, and the barriers that must be overcome in adopting new technologies

General massive gauge theory

The concept of perturbative gauge invariance formulated exclusively by means of asymptotic fields is used to construct massive gauge theories. We consider the interactions of $r$ massive and $s$ massless gauge fields together with $(r+s)$ fermionic ghost and anti-ghost fields. First order gauge invariance requires the introduction of unphysical scalars (Goldstone bosons) and fixes their trilinear couplings. At second order additional physical scalars (Higgs fields) are necessary, their coupling is further restricted at third order. In case of one physical scalar all couplings are determined by gauge invariance, including the Higgs potential. For three massive and one massless gauge field the $SU(2)\times U(1)$ electroweak theory comes out as the unique solution.Comment: 20 pages, latex, no figure

On Gauge Invariance and Spontaneous Symmetry Breaking

We show how the widely used concept of spontaneous symmetry breaking can be explained in causal perturbation theory by introducing a perturbative version of quantum gauge invariance. Perturbative gauge invariance, formulated exclusively by means of asymptotic fields, is discussed for the simple example of Abelian U(1) gauge theory (Abelian Higgs model). Our findings are relevant for the electroweak theory, as pointed out elsewhere.Comment: 13 pages, latex, no figure

“Don’t Have a Cow” . . . or the Restatement (Second)

“Don’t have a cow” is not only Bart Simpson’s mantra but also the admonition of the Michigan Supreme Court in Lenawee County Board of Health v. Messerly. For almost a hundred years, law students and lawyers had a cow to instruct them on the law of mistake: Rose II of Aberlone – the cow in Sherwood v. Walker. Most American lawyers and judges have read Sherwood v. Walker in their contracts casebook and/or have heard their contracts professor talk about the Michigan Supreme Court decision in Sherwood v. Walker and Rose II of Aberlone. Lawyers of a certain age remember Professor Brainerd Currie’s 3,544-word rhymed verse poem, “Rose of Aberlone.” Younger lawyers are more likely to recall Professor Carswell’s song on YouTube, “My Rose.” [..

Don\u27t Have a Cow . . . Or The Restatement (Second)

“Don’t have a cow” is not only Bart Simpson’s mantra but also the admonition of the Michigan Supreme Court in Lenawee County Board of Health v. Messerly. For almost a hundred years, law students and lawyers had a cow to instruct them on the law of mistake: Rose II of Aberlone – the cow in Sherwood v. Walker. Most American lawyers and judges have read Sherwood v. Walker in their contracts casebook and/or have heard their contracts professor talk about the Michigan Supreme Court decision in Sherwood v. Walker and Rose II of Aberlone. Lawyers of a certain age remember Professor Brainerd Currie’s 3,544-word rhymed verse poem, “Rose of Aberlone.” Younger lawyers are more likely to recall Professor Carswell’s song on YouTube, “My Rose.” [..